2) The International Space Station has used a dual-loop ammonia/water-based heat pump to cool the station temperatures. It's been in place for several decades. Heat pumps are a proven technology.
Other satellites have also used heat pumps, such as SES-17 in geostationary orbit https://www.esa.int/Applications/Connectivity_and_Secure_Com...
Looks like some experimental pumps within this region have CoP around 30%: https://www.sciencedirect.com/science/article/abs/pii/S03605...
So you'll need a lot of additional energy to run the pumps. Which will require additional radiator area.
If we want the heat pump's cold end at about 40–65°C, then for each 1MW of GPU heat, we need another 1MW of heat pump power. Now you need 2MW of solar power.
Good news is that the radiator at 227C (500K) can emit about 5× more heat per square meter than at 57C (330K)